研究生: |
李鴻志 |
---|---|
論文名稱: |
在網路模型中探討其分支度的相關性 A Configuration Model with Non-zero Degree Correlations |
指導教授: | 李端興 |
口試委員: |
張正尚
黃之浩 |
學位類別: |
碩士 Master |
系所名稱: |
電機資訊學院 - 通訊工程研究所 Communications Engineering |
論文出版年: | 2012 |
畢業學年度: | 100 |
語文別: | 英文 |
論文頁數: | 30 |
中文關鍵詞: | 分支度 、群聚效應 |
相關次數: | 點閱:52 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
我們這篇論文是隨機網路的一種延伸,目的是根據我們的需要在網路中來產生所需的分支度相關性,我們可以使用任意的分布,這個模型讓我們可以產生特定的群聚係數,我們用模擬來驗證我們的數學分析是正確的,我們也展示了經由改變參數q來簡單的調整群聚係數
The main objective of this paper is to present an extension of the classical configuration model. Like a classical configuration model, the extended configuration model allows
users to specify an arbitrary degree distribution. In addition, the model allows users to specify a positive or a negative assortative coefficient. We derive a closed form for the assortative coefficient of this model. We verify our result with simulations. We show that the assortative coefficient is tunable simply by changing the control parameter q.
[1] A.-L. Barab´asi and R. Albert, “Emergence of Scaling in Random Networks,” Science,
286, 509-512, 1999.
[2] E. A. Bender and E. R. Canfield, “The asymptotic number of labelled graphs with
given degree sequences,”J. Comb. Theory, Ser. A 24, 296, 1978.
[3] M. Bogu˜n´a and R. Pastor-Satorras, “Epidemic spreading in correlated complex networks,”
Physical Review E, 66, 047104, 2002.
[4] M. Bogu˜n´a and R. Pastor-Satorras, “Class of correlated random networks with hidden
variables,” Physical Review E, 68, 036112, 2003.
[5] M. Bogu˜n´a, R. Pastor-Satorras, and A. Vespignani, “Absence of epidemic threshold
in scale-free networks with degree correlations,” Physical Review Letters, Vol. 90,
No. 2, 028701, 2003.
[6] V. M. Egu´ıluz and K. Klemm, “Epidemic threshold in structured scale-free networks,”
Physical Review Letters, Vol. 89, No. 10, 108701, 2002.
[7] Erd˝os and R´enyi , “On Random Graphs,” Publicationes Mathematicicae, 6, 290–297,
1959.
[8] N. Litvak and Remco van der Hofstad, “Degree-degree correlations in random graphs
with heavy-tailed degrees,” 2012.
[9] M. Molloy and B. Reed, “A critical point for random graphs with a given degree
sequence,” Random Struct. Alg. 6, 161-179, 1995.
[10] Y. Moreno, J. B. G´omez, and A. F. Pacheco, “Epidemic incidence in correlated
complex networks,” Physical Review E, 68, 035103(R), 2003.
[11] M.E.J. Newman, “Mixing patterns in networks,” Phys. Rev. E 67, 026126,2003.
[12] M.E.J. Newman, “Networks: An Introduction,” Oxford, 2010.
[13] M. Schl¨apfer and L. Buzna, “Decelerated spreading in degree-correlated networks,”
Physical Review E, 85, 015101(R), 2012.
[14] A. V´azquez and Y. Moreno, “Resilence to damage of graphs with degree correlations,”
Physical Review E, 67, 015101(R), 2003.
[15] R. Xulvi-Brunet and I. M. Sokolov, “Changing correlations in networks: assortativity
and dissortativity,” Acta Physica Polonica B, Vol. 36, No. 5, 1431-1455, 2005.
[16] D. J. Watts and S. H. Strogatz, “Collective Dynamics of ’Small-World’ Networks,”
Nature, 393, 440-442, 1998.
[17] J. Zhou, X. Xu, J. Zhang, J. Sun, M. Small, and J.-A. Lu, “Generating an assortative
network with a given degree distribution,” Intern. J. of Bifuration and Chaos, Vol.
18, No. 11, 3495-3502, 2008.